Abstract
We consider \( \mathcal{N} \) = 1 superconformal field theories in four dimensions possessing an additional conserved spinor current multiplet Sα and study three-point functions involving such an operator. A conserved spinor current multiplet naturally exists in superconformal theories with \( \mathcal{N} \) = 2 supersymmetry and contains the current of the second supersymmetry. However, we do not assume \( \mathcal{N} \) = 2 supersymmetry. We show that the three-point function of two spinor current multiplets and the \( \mathcal{N} \) = 1 supercurrent depends on three independent tensor structures and, in general, is not contained in the three-point function of the \( \mathcal{N} \) = 2 supercurrent. It then follows, based on symmetry considerations only, that the existence of one more Grassmann odd current multiplet in \( \mathcal{N} \) = 1 superconformal field theory does not necessarily imply \( \mathcal{N} \) = 2 superconformal symmetry.
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Buchbinder, E.I., Hutomo, J. & Kuzenko, S.M. Correlation functions of spinor current multiplets in \( \mathcal{N} \) = 1 superconformal theory. J. High Energ. Phys. 2021, 165 (2021). https://doi.org/10.1007/JHEP07(2021)165
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DOI: https://doi.org/10.1007/JHEP07(2021)165